It did not take long after the samsung s3 out a lot of developers who have provided a tool for rooting in these devices, it is almost the same way with other samsung war in general
Make sure your device is a GT-i9300. Can be seen in the Settings> Device> The model number on your Samsung Galaxy S III.
Note : WE WILL NOT BE RESPONSIBLE FOR DAMAGE TO THE CONDITION THAT HAPPENS YOU WILL SAMSUNG GALAXY S3
Step 1: Download ODIN 1.85.
Step 2: Download CF-Root-SGS3-v6.0.zip and extract
Step 3: After CF-Root archive is extracted, the result will be a CF-Root-SGS3-v6.0.tar
Step 4: Do not connect your device to your computer, run the ODIN.
Step 5: Click the PDA, then locate and select file.tar a (extrack file from step 2)
Step 6: input device to the position you Download Mode by turning off, then turn on again by holding down Volume Down + Home + Power together. Once lit, Connect your device to a computer with usb cable
Step 7: Without checking the repartition, click Start, and lets Odin Process for rooting.